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Simplifying 11x2 + -21x + 2 = 0 Reorder the terms: 2 + -21x + 11x2 = 0 Solving 2 + -21x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 0.1818181818 + -1.909090909x + x2 = 0 Move the constant term to the right: Add '-0.1818181818' to each side of the equation. 0.1818181818 + -1.909090909x + -0.1818181818 + x2 = 0 + -0.1818181818 Reorder the terms: 0.1818181818 + -0.1818181818 + -1.909090909x + x2 = 0 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + -1.909090909x + x2 = 0 + -0.1818181818 -1.909090909x + x2 = 0 + -0.1818181818 Combine like terms: 0 + -0.1818181818 = -0.1818181818 -1.909090909x + x2 = -0.1818181818 The x term is -1.909090909x. Take half its coefficient (-0.9545454545). Square it (0.9111570247) and add it to both sides. Add '0.9111570247' to each side of the equation. -1.909090909x + 0.9111570247 + x2 = -0.1818181818 + 0.9111570247 Reorder the terms: 0.9111570247 + -1.909090909x + x2 = -0.1818181818 + 0.9111570247 Combine like terms: -0.1818181818 + 0.9111570247 = 0.7293388429 0.9111570247 + -1.909090909x + x2 = 0.7293388429 Factor a perfect square on the left side: (x + -0.9545454545)(x + -0.9545454545) = 0.7293388429 Calculate the square root of the right side: 0.854013374 Break this problem into two subproblems by setting (x + -0.9545454545) equal to 0.854013374 and -0.854013374.Subproblem 1
x + -0.9545454545 = 0.854013374 Simplifying x + -0.9545454545 = 0.854013374 Reorder the terms: -0.9545454545 + x = 0.854013374 Solving -0.9545454545 + x = 0.854013374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9545454545' to each side of the equation. -0.9545454545 + 0.9545454545 + x = 0.854013374 + 0.9545454545 Combine like terms: -0.9545454545 + 0.9545454545 = 0.0000000000 0.0000000000 + x = 0.854013374 + 0.9545454545 x = 0.854013374 + 0.9545454545 Combine like terms: 0.854013374 + 0.9545454545 = 1.8085588285 x = 1.8085588285 Simplifying x = 1.8085588285Subproblem 2
x + -0.9545454545 = -0.854013374 Simplifying x + -0.9545454545 = -0.854013374 Reorder the terms: -0.9545454545 + x = -0.854013374 Solving -0.9545454545 + x = -0.854013374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9545454545' to each side of the equation. -0.9545454545 + 0.9545454545 + x = -0.854013374 + 0.9545454545 Combine like terms: -0.9545454545 + 0.9545454545 = 0.0000000000 0.0000000000 + x = -0.854013374 + 0.9545454545 x = -0.854013374 + 0.9545454545 Combine like terms: -0.854013374 + 0.9545454545 = 0.1005320805 x = 0.1005320805 Simplifying x = 0.1005320805Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8085588285, 0.1005320805}
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